Welcome to LessWrong! Here are some answers to your questions about MWI:
The space of possibilities in MWI is given by the configuration space of all the particles in the universe. The configuration space consists of every possible arrangement of those particles in physical space. So if a situation can be realized by rearranging the particles, then it is possible according to MWI. There is a slight caveat here, though. Strictly speaking, the only possibilities that are realized correspond to points in configuration space that are, at some point in time, assigned non-zero wavefunction amplitude. There is no requirement that, for an arbitrary initial condition and a finite period of time, every point in configuration space must have non-zero amplitude at some point during that period. Anyway, thinking in terms of worlds is actually a recipe for confusion when it comes to MWI, although at some level it may be unavoidable. The imporant thing to realize is that in MWI “worlds” aren’t fundamental entities. The fundamental object is the wavefunction, and “worlds” are imprecise emergent patterns. Think of “worlds” in MWI the same way you think of “blobs” when you spill some ink. How much ink does there need to be in a particular region before you’d say there’s a blob there? How do you count the number of blobs? These are all vague questions.
MWI does not play nicely with quantum field theory. The whole notion of a false vacuum tunneling into a true vacuum (which, I presume, is what you mean by vacuum decay) only makes sense in the context of QFT. The configuration space of MWI is constructed by considering all the arrangements of a fixed number of particles. So particle number is constant across all worlds and all times in configuration space. Unlike QFT, particles can’t be created or destroyed. So the configuration space of a zero-particle world would be trivial, a single point. If you have more than one particle then all the worlds would have to have more than one particle. None of them would be non-viable or uninteresting. Perhaps it is possible to construct a version of MWI that is compatible with QFT, but I haven’t seen such a construction yet.
Deutsch’s version of MWI (at least at the time he wrote that book) is different from the form of MWI advocated in the sequences. According to the latter, “world-splitting” is just decoherence, the interaction of a quantum system with its environment. But a quantum computer will not work if it decoheres. So according to this version of MWI, in order for a quantum computer to work, we need to make sure it doesn’t split into different worlds. Instead, we would have a quantum computer in a superposed state within a single world, which I guess you can think of as many overlapping and interfering computers embedded in a single larger world. So you’re not really harnessing the computational power of other worlds.
On an appropriate conception of “worlds”, interference does not take place between particles in our world and other worlds. Interference effects are an indication of superposition in our world, a sign of a quantum system that hasn’t decohered. Decoherence destroys interference. It is possible for there to be interference between full-fledged worlds (separate branches of a wave function large enough to contain human beings), but it is astronomically unlikely. You can communicate with other worlds trivially, as long as those worlds are ones which will split off from your world in the future. But otherwise, you’re out of luck.
Welcome to LessWrong! Here are some answers to your questions about MWI:
The space of possibilities in MWI is given by the configuration space of all the particles in the universe. The configuration space consists of every possible arrangement of those particles in physical space. So if a situation can be realized by rearranging the particles, then it is possible according to MWI. There is a slight caveat here, though. Strictly speaking, the only possibilities that are realized correspond to points in configuration space that are, at some point in time, assigned non-zero wavefunction amplitude. There is no requirement that, for an arbitrary initial condition and a finite period of time, every point in configuration space must have non-zero amplitude at some point during that period. Anyway, thinking in terms of worlds is actually a recipe for confusion when it comes to MWI, although at some level it may be unavoidable. The imporant thing to realize is that in MWI “worlds” aren’t fundamental entities. The fundamental object is the wavefunction, and “worlds” are imprecise emergent patterns. Think of “worlds” in MWI the same way you think of “blobs” when you spill some ink. How much ink does there need to be in a particular region before you’d say there’s a blob there? How do you count the number of blobs? These are all vague questions.
MWI does not play nicely with quantum field theory. The whole notion of a false vacuum tunneling into a true vacuum (which, I presume, is what you mean by vacuum decay) only makes sense in the context of QFT. The configuration space of MWI is constructed by considering all the arrangements of a fixed number of particles. So particle number is constant across all worlds and all times in configuration space. Unlike QFT, particles can’t be created or destroyed. So the configuration space of a zero-particle world would be trivial, a single point. If you have more than one particle then all the worlds would have to have more than one particle. None of them would be non-viable or uninteresting. Perhaps it is possible to construct a version of MWI that is compatible with QFT, but I haven’t seen such a construction yet.
Deutsch’s version of MWI (at least at the time he wrote that book) is different from the form of MWI advocated in the sequences. According to the latter, “world-splitting” is just decoherence, the interaction of a quantum system with its environment. But a quantum computer will not work if it decoheres. So according to this version of MWI, in order for a quantum computer to work, we need to make sure it doesn’t split into different worlds. Instead, we would have a quantum computer in a superposed state within a single world, which I guess you can think of as many overlapping and interfering computers embedded in a single larger world. So you’re not really harnessing the computational power of other worlds.
On an appropriate conception of “worlds”, interference does not take place between particles in our world and other worlds. Interference effects are an indication of superposition in our world, a sign of a quantum system that hasn’t decohered. Decoherence destroys interference. It is possible for there to be interference between full-fledged worlds (separate branches of a wave function large enough to contain human beings), but it is astronomically unlikely. You can communicate with other worlds trivially, as long as those worlds are ones which will split off from your world in the future. But otherwise, you’re out of luck.
Thanks for the answers, Pragmatist. I’m still fairly confused. But I’ll read more in the sequence and elsewhere. I appreciate the effort/time.